THE USE OF THE OPERATOR METHOD IN NONSTATIONARY HEAT CONDUCTION OF INHOMOGENEOUS ELEMENTS OF ASSEMBLIES AND MECHANISMS OF FOOD PRODUCTION

Abstract

The  use of the operator method for the study of heat phenomena in  inhomogeneous plate elements equipment of  food industry, was proposed. At the same time the inhomogeneous plate, thermophysical characteristics of  which are a function of polar coordinates , was considered. With the submission of the temperature of the plate due to  its integral characteristics in the operator form an interconnected system of differential equations of heat conductivity of  infinitely high order, was  obtained. For a complete formulation of  the problem of nonstationary heat conduction, generalized terms from all surfaces of the plate, was recorded. This allows  combining  all possible variations of the conditions of  heat transfer and forming their  linear combinations. As particular cases  heat equations  for inhomogeneous flat surfaces are given the heat flux density and transient temperature of different environments by Newton's law, were considered. Expanding heat equation operators in the resulting in the power series, significantly simplified approximation of the heat equation, in particular, no more than the third degree of decomposition,was obtained. In this case, the interconnected system of differential equations of  heat conductivity is allows spliting up, which significantly simplifies  obtaining  the general  solution to  the problem of heat conductivity  integral Fourier and Laplace transformations.